The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to methods for acquiring magnetic resonance imaging (xe2x80x9cMRIxe2x80x9d) data using a sensitivity encoding (xe2x80x9cSENSExe2x80x9d) technique.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or xe2x80x9ctippedxe2x80x9d, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx Gy and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The present invention will be described with reference to a variant of the well known Fourier transform (FT) imaging technique, which is frequently referred to as xe2x80x9cspin-warpxe2x80x9d. The spin-warp technique is discussed in an article entitled xe2x80x9cSpin-Warp NMR Imaging and Applications to Human Whole-Body Imagingxe2x80x9d by W. A. Edelstein et al., Physics in Medicine and Biology, Vol. 25, pp. 751-756 (1980). It employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of NMR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (2DFT), for example, spatial information is encoded in one direction by applying a phase encoding gradient (Gy) along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient (Gx) in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT image acquisition, a series of pulse sequences is performed in which the magnitude of the phase encoding gradient pulse Gy in the pulse sequence is incremented (xcex94Gy). The resulting series of views that is acquired during the scan form an NMR image data set from which an image can be reconstructed. The acquisition of each phase encoded view requires a finite amount of time, and the more views that are required to obtain an image of the prescribed field of view and spatial resolution, the longer the total scan time.
Reducing scan time is a very important objective in MRI. In addition to improved patient comfort, shorter scan times free up the imaging system for more patients and reduces image artifacts caused by patient motion. SENSE (SENSitivity Encoding) is a technique described by K. P. Pruessmann, et al., xe2x80x9cSENSE: Sensitivity Encoding for Fast MRIxe2x80x9d, J. Magn. Reson. 42, 952-962 (1999), which reduces MRI data acquisition time by using multiple local coils. The idea is to reduce acquisition time by increasing the step size (xcex94Gy) between phase encoding views, or equivalently, by reducing the field of view. In either case, the total number of views is reduced with a consequent reduction in scan time. If the object extends outside the reduced field of view, however, aliasing or wrap-around occurs in the phase encoding direction. The SENSE technique removes this aliasing by using knowledge of the surface coil receive field (also called sensitivities) to find the unaliased spin distribution.
For simplicity, one can consider the image intensity variation only in the phase encoding direction, which may be, for example, the y direction. N local coils with B1 receive field sensitivities Sj(y) where j=0, 1, . . . Nxe2x88x921 are used to acquire the NMR data. The reconstructed image intensity for each local coil is weighted by its receive field. If the reconstructed image for coil j is lj(y), and the ideal proton density distribution, including T1 and T2 weighting factors, is M(y), then
Ij(y)=Sj(y)M(y)xe2x80x83xe2x80x83(1) 
Aliasing or replication occurs in an MR image in the phase encode direction. The replication distance is the same as the field of view. If the field of view D is chosen such that the subject is completely contained within this field of view, the replicates of the subject do not overlap and no artifact results in the reconstructed image. If the field of view is reduced in the y direction by a factor of L, the scan time is also correspondingly reduced by a factor of L. However, now the reconstructed image is aliased or replicated in the y direction at multiples of xcex94y=D/L and aliasing replicates now overlap with resulting loss of diagnostic utility. Mathematically, the image intensity is now
Ij(y)=Sj(y)M(y)+Sj(y+xcex94y)M(y+xcex94y)+ . . . +Sj(y+(Lxe2x88x921)xcex94y)M(y+(Lxe2x88x921)xcex94y),xe2x80x83xe2x80x83(2) 
for 0xe2x89xa6y xcex94y. If the local coil sensitivities Sj(y) are known, and if Nxe2x89xa7L, the proton distribution M(y) can be obtained by solving the resulting N equations. In matrix form equation (2) can be written
I=SM,xe2x80x83xe2x80x83(3) 
where:                               I          =                      [                                                                                                      I                      0                                        ⁡                                          (                      y                      )                                                                                                                                                              I                      1                                        ⁡                                          (                      y                      )                                                                                                                    ⋮                                                                                                                        I                                              N                        -                        1                                                              ⁡                                          (                      y                      )                                                                                            ]                          ,                            (        4        )                                          M          =                      [                                                                                M                    ⁡                                          (                      y                      )                                                                                                                                        M                    ⁡                                          (                                              y                        +                                                  Δ                          ⁢                                                      xe2x80x83                                                    ⁢                          y                                                                    )                                                                                                                    ⋮                                                                                                  M                    (                                          y                      +                                                                        (                                                      L                            -                            1                                                    )                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        y                                                                                                                  ]                          ,                  
                ⁢        and                            (        5        )                                S        =                              [                                                                                                      S                      0                                        ⁡                                          (                      y                      )                                                                                                                                                          S                        0                                            ⁡                                              (                                                  y                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            y                                                                          )                                                              ⁢                                          xe2x80x83                                        ⁢                    …                    ⁢                                          xe2x80x83                                        ⁢                                                                  S                        0                                            ⁡                                              (                                                  y                          +                                                                                    (                                                              L                                -                                1                                                            )                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            y                                                                          )                                                                                                                                                                                    S                      1                                        ⁡                                          (                      y                      )                                                                                                                                                          S                        1                                            ⁡                                              (                                                  y                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            y                                                                          )                                                              ⁢                                          xe2x80x83                                        ⁢                    …                    ⁢                                          xe2x80x83                                        ⁢                                                                  S                        1                                            ⁡                                              (                                                  y                          +                                                                                    (                                                              L                                -                                1                                                            )                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            y                                                                          )                                                                                                                                          ⋮                                                                      xe2x80x83                                                                                                                                          S                                              N                        -                        1                                                              ⁡                                          (                      y                      )                                                                                                                                                          S                                                  N                          -                          1                                                                    ⁡                                              (                                                  y                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            y                                                                          )                                                              ⁢                                          xe2x80x83                                        ⁢                    …                    ⁢                                          xe2x80x83                                        ⁢                                                                  S                                                  N                          -                          1                                                                    ⁡                                              (                                                  y                          +                                                                                    (                                                              L                                -                                1                                                            )                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            y                                                                          )                                                                                                                  ]                    .                                    (        6        )            
Note that I and M are Nxc3x971 and Lxc3x971 dimensional matrices, respectively, while S has dimensions Nxc3x97L. The solution of equation (3) is efficiently determined using the pseudoinverse of S. Denoting the complex conjugate transpose of S as S* then
M=(S*S)xe2x88x921S*Ixe2x80x83xe2x80x83(7) 
Typically, the coil sensitivity values Sj(y) are obtained by performing two calibration scans. The calibration scans are performed with the subject of the scan in place and throughout the full prescribed field of view. Calibration data from one scan is acquired with the body RF coil which has a substantially homogeneous receive field, and data from the second calibration scan is acquired using each of the N local coils. The B1 field sensitivity of each local coil is obtained by taking the ratio of the complex calibration images acquired with the body coil and each of the surface coils. For example, if             I      j      cal        ⁡          (      y      )        ⁢      xe2x80x83    ⁢  and  ⁢      xe2x80x83    ⁢            I      body      cal        ⁡          (      y      )      
are the respective full field of view calibration images obtained with surface coil j and the calibration image acquired with the body coil, the sensitivity of the surface coil j is estimated as                                           S            j                    ⁡                      (            y            )                          =                                                            I                j                cal                            ⁡                              (                y                )                                                                    I                body                cal                            ⁡                              (                y                )                                              .                                    (        8        )            
Note that the complex magnetization term M(y) drops out of the ratio in equation (8) if the body coil and the surface coil scans are performed using the same scan prescription. In this case, the reconstructed images have the proton distribution weighted by the body coil B1 field which is normally very homogeneous over the field of view.
The calibration procedure is performed while the subject is in place and the time required to obtain the calibration data is an offset against the time gained by using the SENSE technique. Because the reception fields must be estimated at each imaging plane and throughout the prescribed field of view, many calibration scans are required to acquire the necessary data for the above equations. Various methods of reducing the calibration time are known to those skilled in the art. For example, calibration time can be reduced by reducing spatial resolution, thus requiring fewer phase encoding steps during the calibration. As another example, instead of measuring the sensitivity at each desired imaging plane, the sensitivity can be measured at a small number of fixed, widely separate planes, and interpolation may be used to estimate the sensitivity at the desired planes. The problem is that such obvious methods compromise the accuracy of the sensitivity matrix S in equation (6) if carried too far. One problem to be solved therefore, is how to reduce the calibration time without compromising the accuracy of the sensitivity matrix S.
Another difficulty with the current method for estimating the coil sensitivity matrix S is corruption of the calibration data due to undesirable coupling between the body RF coil and the local coils. It is impractical to remove the local coils from the subject during acquisition of the calibration data with the body RF coil, and the mutual inductance therebetween often couples undesirable signals from the local coils into the body RF coil data. Extra ordinary measures must be taken to reduce this coupling so that accurate body RF coil calibration data can be acquired to solve equation (8).
One solution to the problems associated with the acquisition of body coil calibration data is to eliminate the need for such data. Such a solution is disclosed by J. Wang et al., xe2x80x9cA SMASH/SENSE Related Method Using Ratios of Array Coil Profilesxe2x80x9d, Proc. Of The 7th ISMRM, Philadelphia, Pa. 1648 (1999), in which the body coil calibration scans are eliminated. Instead of the sensitivity defined by the ratio of surface coil to body coil intensity, a new reduced sensitivity is defined consisting of the ratios of the various local coil intensities. The resulting image after SENSE unwrapping is then weighted by the various local coil sensitivities. A disadvantage of this method is increased reconstruction time. Since SENSE reconstruction is already computationally intensive, this is a major drawback.
The present invention is a method for estimating the coil sensitivity matrix S for use in a sensitivity encoded MRI scan. More particularly, the sensitivity S for a coil j in an array of N coils is determined by acquiring calibration data with all N coils, reconstructing calibration images ICAL for each of the N coils; and producing a sensitivity image Sj for each local coil j by calculating the ratio of the calibration image for the local coil j and the sum of all N local coil calibration images. The sensitivity matrix S is formed by combining the local coil sensitivity images Sj. There is no need to acquire body coil calibration data and the resulting sensitivity matrix S can be employed in the SENSE reconstruction method.